Geodesic
Some properties of the complexification of the KdV equation
Izvestiya. Mathematics , Tome 39 (1992) no. 3, pp. 1251-1261.

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An integrable complexification of the hierarchy of the KdV equation is constructed. A countable set of first integrals is found, along with the evolution of the scattering data for the complexification of the KdV equation obtained in [1]. Hirota's method is used to obtain some exact solutions of this equation. A representation of the complexification of the KdV equation as an equation of zero curvature is indicated. 
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T. V. Red'kina. Some properties of the complexification of the KdV equation. Izvestiya. Mathematics , Tome 39 (1992) no. 3, pp. 1251-1261. http://geodesic.mathdoc.fr/item/IM2_1992_39_3_a7/

[1] Bogoyavlenskii O. I., “Oprokidyvayuschiesya solitony. III”, Izv. AN SSSR. Ser. matem., 54:1 (1989), 123–131 | MR

[2] Laks P. D., “Integraly nelineinykh evolyutsionnykh uravnenii i uedinennoi volny”, Matematika, 13:5 (1968), 128–150

[3] Zakharov V. E., Shabat A. B., “Skhema integrirovaniya nelineinykh evolyutsionnykh uravnenii matematicheskoi fiziki metodom obratnoi zadachi rasseyaniya. I”, Funkts. analiz i ego prilozh., 8:3 (1974), 43–53 | MR | Zbl

[4] Zakharov V. E., Manakov S. V., “Teoriya rezonansnogo vzaimodeistviya volnovykh paketov v nelineinykh sredakh”, Pisma v ZhETF, 69 (1975), 1654–1673 | MR

[5] Iwasaki K., “Scattering theory for 4-th order differential operators. I, II”, Journ. Mathem. Japan, 22:1 (1988), 1–97 | MR

[6] S. P. Novikov (ed.), Teoriya solitonov, Nauka, M., 1980 | MR

[7] Ablowitz M. J., Segur H., “Exact linearization of a Panileve transcendent”, Phys. Rev. Lett., 38 (1977), 1103–1106 | DOI | MR

[8] Hirota R., “Nonlinear partial difference equations. V. Nonlinear equations reducible to linear equations”, Journ. Phys. Soc. Japan, 46 (1979), 312–319 | DOI | MR

[9] Fordy A. P., Gibbons J., “Factorization of oparators. I. Miura transformations”, Journ. Mathem. Phys., 21:10 (1980), 2508–2510 | DOI | MR | Zbl

[10] Nyuell A., Solitony v matematike i fizike, per. s angl., Mir, M., 1989 | MR